Given n Z+, let the set M(n, k) Zn2 contain the maximum number of code words of length n, where the minimum distance between code

Given n ˆˆ Z+, let the set M(n, k) Š† Zn2 contain the maximum number of code words of length n, where the minimum distance between code words is 2k + 1. Prove that

(The upper bound on |M(n, k)| is called the Hamming bound; the lower bound is referred to as the Gilbert bound.)

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